Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2

March 21st 2007, 04:02 PM

ThePerfectHacker

Quote:

Originally Posted by Rimas

Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2

3,6,9,12,15,....,999
How many? Answer (333)

Now list all those divisible by 2:
6,12,18,....,996
How many? Answer (83)

Subtract them to get answer.

March 27th 2007, 03:59 PM

ceasar_19134

Rimas and I are friends, and you seem to have read the problem wrong like I did intially. The problem asks for the sum of the integers, not how many integers.

I already determined that the sum of all integers divisible by 3 and 2 is 82,170 if that helps any.

March 27th 2007, 11:09 PM

DivideBy0

To solve this problem, you have to know this formula: n/2 * (a + L), where a is the first number in the series, L is the last number in the series, and n is the number of numbers in the series. It gives the sum of the series.

So... you have to sum every multiple of 3 first. As there are 333 of them, the first is 3, and the last is 999, sub that in to find the sum:

333/2 * (3 + 999) = 166833

Next, subtract all the number divisible by both 2 and 3 (that is, numbers divisible by 2*3 = numbers divisible by 6). As there are 166 of them, the first is 6 and the last is 996, sub that in to find the sum:

166/2 * (6 + 996) = 83166

Now, simply subtract 83166 from 166833:

166833 - 83166 = 83667 :cool:

If you have any questions regarding the formula or anything else feel free to ask.

March 31st 2007, 04:34 AM

Soroban

Hello, Rimas!

Quote:

Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2